The solution of $(1-x^2)\frac{dy}{dx}+2xy-x\sqrt{1-x^2}=0$, is

Important Questions on Differential Equations - II

HARD

JEE Main

IMPORTANT

Eduwiser's INTEGRAL CALCULUS For JEE Main & Advanced>Chapter 10 - Differential Equations - II>EXERCISE>Q 38

The solution of differential equation $x{y}_2-(2x-1)y_1+(x-1)y=0$ is

HARD

JEE Main

IMPORTANT

Eduwiser's INTEGRAL CALCULUS For JEE Main & Advanced>Chapter 10 - Differential Equations - II>EXERCISE>Q 39

The solution of $y(2xy+e^x)dx-e^{x}dy = 0$ is

MEDIUM

JEE Main

IMPORTANT

Eduwiser's INTEGRAL CALCULUS For JEE Main & Advanced>Chapter 10 - Differential Equations - II>EXERCISE>Q 40

The largest value of '$c$' such that there exists a differentiable function $f\left(x\right)$ for $-c<x<c$ that satisfies the equation $y_1=1+y^2$ with $f\left(0\right)=0$ is

MEDIUM

JEE Main

IMPORTANT

Eduwiser's INTEGRAL CALCULUS For JEE Main & Advanced>Chapter 10 - Differential Equations - II>EXERCISE>Q 42

The degree and order of the differential equation of the family of all parabolas whose axis is $x$-axis are respectively

MEDIUM

JEE Main

IMPORTANT

Eduwiser's INTEGRAL CALCULUS For JEE Main & Advanced>Chapter 10 - Differential Equations - II>EXERCISE>Q 43

The solution of the differential equation $(1+y^2)+(x-e^{{\tan }^{-1}y})\frac{dy}{dx}=0$ is

MEDIUM

JEE Main

IMPORTANT

Eduwiser's INTEGRAL CALCULUS For JEE Main & Advanced>Chapter 10 - Differential Equations - II>EXERCISE>Q 44

The differential equation for the family of curves $x^2+ y^2-2ay=0$, where $a$ is an arbitrary constant is

HARD

JEE Main

IMPORTANT

Eduwiser's INTEGRAL CALCULUS For JEE Main & Advanced>Chapter 10 - Differential Equations - II>EXERCISE>Q 45

The solution of the differential equation $ydx+(x+x^{2}y)dy=0$ is

MEDIUM

JEE Main

IMPORTANT

Eduwiser's INTEGRAL CALCULUS For JEE Main & Advanced>Chapter 10 - Differential Equations - II>EXERCISE>Q 46

If $x\frac{dy}{dx}=y(\log y-\log x+1)$, then the solution of the equation is