Let y=y(x) be the solution of the differential equation x⁴dy+(4x³y+2 sin x)dx=0, x>0, y((π)/2)=0. Then π⁴y((π)/3) is equal to:

Differential Equations: JEE Main 2026 Mathematics question

JEE Main 2026 · 23 Jan, Morning shift · Q6

JEE Main 202623 Jan, Morning shiftMathematicsEasyDifferential Equations163× since 2002

Let

y=y(x)

be the solution of the differential equation

x^4dy+(4x^3y+2\sin x)dx=0

x>0

y\left(\frac{\pi}{2}\right)=0

. Then

\pi^4y\left(\frac{\pi}{3}\right)

is equal to :

JEE Main 2026 · 23 Jan, Morning shift · Q6

JEE Main 202623 Jan, Morning shiftMathematicsEasyDifferential Equations163× since 2002

Let

y=y(x)

be the solution of the differential equation

x^4dy+(4x^3y+2\sin x)dx=0

x>0

y\left(\frac{\pi}{2}\right)=0

. Then

\pi^4y\left(\frac{\pi}{3}\right)

is equal to :