Solve the differential equation Differential Equations Miscellaneous Exercise 10.

Name: Solve the differential equation Differential Equations Miscellaneous Exercise 10.
Uploaded: Mon, 2019-06-10 18:11
Description: Solve the differential equation Differential Equations Miscellaneous Exercise 10.

Q10. Solve the differential equation $ye^\frac{x}{y}dx = \left(e^\frac{x}{y} + y^2 \right )dy\ (y \neq 0)$

Answers (1)

Given,

$y e^{\frac{x}{y}} d x = (e^{\frac{x}{y}} + y^{2}) d y$
$y e^{\frac{x}{y}} \frac{d x}{d y} = e^{\frac{x}{y}} + y^{2}$
$⟹ e^{\frac{x}{y}} [y \frac{d x}{d y} - x] = y^{2}$
$⟹ \frac{e^{\frac{x}{y}} [y \frac{d x}{d y} - x]}{y^{2}} = 1$
Let $e^{\frac{x}{y}} = t$

Differentiating it w.r.t. $y$ , we get,

$\frac{d}{d y} e^{\frac{x}{y}} = \frac{d t}{d y}$
$⟹ e^{\frac{x}{y}} \cdot \frac{d}{d y} (\frac{x}{y}) = \frac{d t}{d y}$
$⟹ \frac{e^{\frac{x}{y}} [y \frac{d x}{d y} - x]}{y^{2}} = \frac{d t}{d y}$
Thus from these two equations, we get,
$\frac{d t}{d y} = 1$

$⟹ \int d t = \int d y$
$⟹ t = y + C$
$⟹ e^{\frac{x}{y}} = y + C$

Posted by

HARSH KANKARIA

View full answer

Crack CUET with india's "Best Teachers"

HD Video Lectures
Unlimited Mock Tests
Faculty Support

Exams

Colleges

Predictors

Resources

Quick links

Quick Links

Exams

Colleges

Resources

Colleges

Resources

Exams

Exams

Colleges

Resources

Diploma Colleges

Other Exams

Exams

Resources

Upcoming Events

Exams

Top Schools

Products & Resources

NCERT Study Material

Top Countries

Student Visas

Exams

Colleges

Exams

Colleges

Upcoming Events

Resources

Exams

Colleges & Courses

Predictors

Resources

Online Courses

Products

Engineering Preparation

Medical Preparation

Top Streams

Specializations

Resources

Top Providers

Exams

Colleges

Predictors

Resources

Resources

Exams

Colleges

Predictors & E-Books

Exams

Predictors & Articles

Colleges

Resources

Exams

Colleges

Resources

Top Courses & Careers

Colleges

Exams

Resources

Get Answers to all your Questions

Q10. Solve the differential equation

Answers (1)

Posted by

HARSH KANKARIA

Crack CUET with india's "Best Teachers"

Similar Questions

Trending Articles/News

Latest Question

Ask your Query

Welcome Back :)

Register to post Answer

Welcome Back :)

Q10. Solve the differential equation $ye^\frac{x}{y}dx = \left(e^\frac{x}{y} + y^2 \right )dy\ (y \neq 0)$