Let the solution curve y=y(x) of the differential equation (d y)/(~d x)-(3 x⁵ tan ⁻¹(x³))/((1+x⁶)^(3 / 2)) y=2 x exp \(x³- tan ⁻¹ x³)/(√((1+x⁶))) pass through the origin. Then y(1) is equal to:

Differential Equations: JEE Main 2023 Mathematics question

JEE Main 2023 · 30 Jan, Morning shift · Q3554

JEE Main 202330 Jan, Morning shiftMathematicsMediumDifferential Equations163× since 2002

Let the solution curve

y=y(x)

of the differential equation

\frac{\mathrm{d} y}{\mathrm{~d} x}-\frac{3 x^{5} \tan ^{-1}\left(x^{3}\right)}{\left(1+x^{6}\right)^{3 / 2}} y=2 x \exp \left\{\frac{x^{3}-\tan ^{-1} x^{3}}{\sqrt{\left(1+x^{6}\right)}}\right\} \text { pass through the origin. Then } y(1) \text { is equal to : }

JEE Main 2023 · 30 Jan, Morning shift · Q3554

JEE Main 202330 Jan, Morning shiftMathematicsMediumDifferential Equations163× since 2002

Let the solution curve

y=y(x)

of the differential equation

\frac{\mathrm{d} y}{\mathrm{~d} x}-\frac{3 x^{5} \tan ^{-1}\left(x^{3}\right)}{\left(1+x^{6}\right)^{3 / 2}} y=2 x \exp \left\{\frac{x^{3}-\tan ^{-1} x^{3}}{\sqrt{\left(1+x^{6}\right)}}\right\} \text { pass through the origin. Then } y(1) \text { is equal to : }