Q. 275.0( 1 Vote )

# Solve the differe

Given, A differential equation x2 dy + y(x + y)dx = 0

To Find: Find the particular solution at y = 1 and x = 1

Explanation: We have given

x2 dy + y(x + y)dx = 0

x2 dy = - y(x + y)dx   …(i)

Let F(x, y) = To check that, given differential equation is homogenous ,

Put x = λx and y = λy in F(x, y)

Then, Now, Taking λ2 common from both numerator and denominator In F(x, y) If λ0, then F(x, y) is a homogenous function of degree zero.

Let’s put y = vx in equation(i)

On differentiating y , we get …(ii)

Now, Compare the equation (i) and (ii) Taking x2 as common from the numerator and denominator    Now, Integrating both sides  Solve dv by completing the square method  We know, , then      Now, putting     Now, Put x = 1 and y = 1  1 = 3C Put the value of C  Hence, Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

Solve the differeMathematics - Board Papers

Solve the followiMathematics - Board Papers

Find the particulMathematics - Board Papers

Show that the difMathematics - Board Papers

Solve the differeMathematics - Board Papers

Find the particulMathematics - Board Papers