Solution of the differential equation $\

CUET Preparation Today

Start Free Mocks

Home Questions FGEC96ZZZ4

Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Differential Equations

Question:

Solution of the differential equation $\frac{dy}{dx}+\frac{3x}{2y}=0$ with y(1)= 1 is :

Options:

$2y^2+3x^2=5$

$3x^2-2y^2=5$

$2x^2+3y^2-5=0$

$2x^2+3y^2+5=0$

Correct Answer:

$2y^2+3x^2=5$

Explanation:

The correct answer is Option (1) → $2y^2+3x^2=5$

$\frac{dy}{dx}+\frac{3x}{2y}⇒∫2ydy=∫-3xdx$

so $y^2=-\frac{3}{2}x^2+C$

at $x = 1,y=1$

$⇒1=-\frac{3}{2}+C⇒C=\frac{5}{2}$

so eq. ⇒ $y^2=-\frac{3}{2}x^2+\frac{5}{2}$

$⇒2y^2+3x^2=5$