Top 50 Most Repeated DIFFERENTIAL EQUATIONS PYQs | JEE MAINS
A curated collection of the most important questions from DIFFERENTIAL EQUATIONS, fully solved with step-by-step concepts to prepare for JEE MAINS.
A curated collection of the most important questions from DIFFERENTIAL EQUATIONS, fully solved with step-by-step concepts to prepare for JEE MAINS.
Separate variables and integrate: $\ln|y| = \ln|x| + C$, apply IC....
Read Full Step-by-Step Solution →The given equation is homogeneous. Substituting $y = vx$ gives $\frac{dy}{dx} = v + x\frac{dv}{dx}$. The right-hand side becomes $\frac{x^2 + (vx)^2}{...
Read Full Step-by-Step Solution →Highest derivative is $d^2y/dx^2$ (order 2); its power is 3 (degree 3)....
Read Full Step-by-Step Solution →Use $P(t) = P_0 e^{kt}$; solve
Integrating factor is $e^{2x}$; multiply and integrate to get solution....
Read Full Step-by-Step Solution →Separate variables: $\frac{dy}{y} = \frac{dx}{x}$, integrate: $\ln y = \ln x + C$, apply IC: $y = x$, so $y(e) = e \approx 2.72$....
Read Full Step-by-Step Solution →Step 1: Since the surface is passing through the point $(1, 1, 1)$, we can substitute these values into the equation of the surface to get
Step 1: Given the differential equation $\frac{dy}{dx} = \frac{2x}{y}$, we can rewrite it as $\frac{dy}{y} = \frac{2x}{y}dx$....
Read Full Step-by-Step Solution →Bernoulli equation with $n=2$, use $v = y^{1-2} = y^{-1}$....
Read Full Step-by-Step Solution →Separate variables: $\frac{dy}{y} = \frac{dx}{x}$, integrate and apply $y(1)=1$....
Read Full Step-by-Step Solution →The highest derivative is \(d^2y/dx^2\) → order 2. The equation contains \((dy/dx)^2\) which makes the degree 2 (since the highest power of the highes...
Read Full Step-by-Step Solution →Integrating factor is $e^{\int (2/x) dx} = e^{2\ln x} = x^2$....
Read Full Step-by-Step Solution →Separate variables: $\frac{dy}{y^{2}} = (x^{2}+1)dx$. Integrate: $-\frac{1}{y}=\frac{x^{3}}{3}+x+C$. Use $y(0)=1$ to get $C=-1$. Hence $-\frac{1}{y}=\...
Read Full Step-by-Step Solution →Separate variables and integrate: $\ln|y| = \ln|x| + C$, apply IC....
Read Full Step-by-Step Solution →The given equation is homogeneous. Substituting $y = vx$ gives $\frac{dy}{dx} = v + x\frac{dv}{dx}$. The right-hand side becomes $\frac{x^2 + (vx)^2}{...
Read Full Step-by-Step Solution →Highest derivative is $d^2y/dx^2$ (order 2); its power is 3 (degree 3)....
Read Full Step-by-Step Solution →Use $P(t) = P_0 e^{kt}$; solve
Integrating factor is $e^{2x}$; multiply and integrate to get solution....
Read Full Step-by-Step Solution →Separate variables: $\frac{dy}{y} = \frac{dx}{x}$, integrate: $\ln y = \ln x + C$, apply IC: $y = x$, so $y(e) = e \approx 2.72$....
Read Full Step-by-Step Solution →Step 1: Since the surface is passing through the point $(1, 1, 1)$, we can substitute these values into the equation of the surface to get
Step 1: Given the differential equation $\frac{dy}{dx} = \frac{2x}{y}$, we can rewrite it as $\frac{dy}{y} = \frac{2x}{y}dx$....
Read Full Step-by-Step Solution →Bernoulli equation with $n=2$, use $v = y^{1-2} = y^{-1}$....
Read Full Step-by-Step Solution →Separate variables: $\frac{dy}{y} = \frac{dx}{x}$, integrate and apply $y(1)=1$....
Read Full Step-by-Step Solution →The highest derivative is \(d^2y/dx^2\) → order 2. The equation contains \((dy/dx)^2\) which makes the degree 2 (since the highest power of the highes...
Read Full Step-by-Step Solution →Integrating factor is $e^{\int (2/x) dx} = e^{2\ln x} = x^2$....
Read Full Step-by-Step Solution →Separate variables: $\frac{dy}{y^{2}} = (x^{2}+1)dx$. Integrate: $-\frac{1}{y}=\frac{x^{3}}{3}+x+C$. Use $y(0)=1$ to get $C=-1$. Hence $-\frac{1}{y}=\...
Read Full Step-by-Step Solution →Separate variables and integrate: $\ln|y| = \ln|x| + C$, apply IC....
Read Full Step-by-Step Solution →The given equation is homogeneous. Substituting $y = vx$ gives $\frac{dy}{dx} = v + x\frac{dv}{dx}$. The right-hand side becomes $\frac{x^2 + (vx)^2}{...
Read Full Step-by-Step Solution →Highest derivative is $d^2y/dx^2$ (order 2); its power is 3 (degree 3)....
Read Full Step-by-Step Solution →Use $P(t) = P_0 e^{kt}$; solve
Integrating factor is $e^{2x}$; multiply and integrate to get solution....
Read Full Step-by-Step Solution →Separate variables: $\frac{dy}{y} = \frac{dx}{x}$, integrate: $\ln y = \ln x + C$, apply IC: $y = x$, so $y(e) = e \approx 2.72$....
Read Full Step-by-Step Solution →Step 1: Since the surface is passing through the point $(1, 1, 1)$, we can substitute these values into the equation of the surface to get
Step 1: Given the differential equation $\frac{dy}{dx} = \frac{2x}{y}$, we can rewrite it as $\frac{dy}{y} = \frac{2x}{y}dx$....
Read Full Step-by-Step Solution →Bernoulli equation with $n=2$, use $v = y^{1-2} = y^{-1}$....
Read Full Step-by-Step Solution →Separate variables: $\frac{dy}{y} = \frac{dx}{x}$, integrate and apply $y(1)=1$....
Read Full Step-by-Step Solution →The highest derivative is \(d^2y/dx^2\) → order 2. The equation contains \((dy/dx)^2\) which makes the degree 2 (since the highest power of the highes...
Read Full Step-by-Step Solution →Integrating factor is $e^{\int (2/x) dx} = e^{2\ln x} = x^2$....
Read Full Step-by-Step Solution →Separate variables: $\frac{dy}{y^{2}} = (x^{2}+1)dx$. Integrate: $-\frac{1}{y}=\frac{x^{3}}{3}+x+C$. Use $y(0)=1$ to get $C=-1$. Hence $-\frac{1}{y}=\...
Read Full Step-by-Step Solution →Separate variables and integrate: $\ln|y| = \ln|x| + C$, apply IC....
Read Full Step-by-Step Solution →The given equation is homogeneous. Substituting $y = vx$ gives $\frac{dy}{dx} = v + x\frac{dv}{dx}$. The right-hand side becomes $\frac{x^2 + (vx)^2}{...
Read Full Step-by-Step Solution →Highest derivative is $d^2y/dx^2$ (order 2); its power is 3 (degree 3)....
Read Full Step-by-Step Solution →Use $P(t) = P_0 e^{kt}$; solve
Integrating factor is $e^{2x}$; multiply and integrate to get solution....
Read Full Step-by-Step Solution →Separate variables: $\frac{dy}{y} = \frac{dx}{x}$, integrate: $\ln y = \ln x + C$, apply IC: $y = x$, so $y(e) = e \approx 2.72$....
Read Full Step-by-Step Solution →Step 1: Since the surface is passing through the point $(1, 1, 1)$, we can substitute these values into the equation of the surface to get
Step 1: Given the differential equation $\frac{dy}{dx} = \frac{2x}{y}$, we can rewrite it as $\frac{dy}{y} = \frac{2x}{y}dx$....
Read Full Step-by-Step Solution →