MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Variable Separable Method

Solve the dif...

Question

Solve the differential equation
$x y \frac{d y}{d x} = \frac{1 + y^{2}}{1 + x^{2}} (1 + x + x^{2})$

Open in App

Solution

Given,

$x y \frac{d y}{d x} = \frac{1 + y^{2}}{1 + x^{2}} (1 + x + x^{2})$
$\frac{y}{1 + y^{2}} d y = \frac{1 + x + x^{2}}{x (1 + x^{2})} d x$
$\frac{1}{2} \int \frac{2 y}{1 + y^{2}} d y = \int \frac{1}{x} d x + \int \frac{1}{1 + x^{2}} d x$
$\frac{1}{2} log | 1 + y^{2} | = log x + {tan}^{- 1} x + c$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Solve the following differential equation:

\sqrt{1 + x^{2} + y^{2} + x^{2} y^{2}} + x y \frac{d y}{d x} = 0

Q. Solve the differential equation

y^{2} + x^{2} \frac{d y}{d x} = x y \frac{d y}{d x}

.

Q. Find the solution of

x y \frac{d y}{d x} = \frac{1 + y^{2}}{1 + x^{2}} (1 + x + x^{2})

.

Q. The solution of differential equation

4 x y \frac{d y}{d x} = \frac{3 {(1 + x)}^{2} (1 + y^{2})}{(1 + x^{2})}

Q. Solve the differential equation,

(x^{2} + x y) d y = (x^{2} + y^{2}) d x

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Methods of Solving First Order, First Degree Differential Equations

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Variable Separable Method

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon