# GATE Papers >> Mechanical >> 2019 >> Question No 13

Question No. 13

For the equation $\frac{\mathrm dy}{\mathrm dx}$ + 7x2 = 0, if (0) = 3/7, then the value of (1) is

##### Answer : (C) $\frac37e^{-7/3}$

Solution of Question No 13 of GATE 2019 Mechanical Paper

$\begin{array}{l}\frac{\mathrm{dy}}{\mathrm{dx}}+7\mathrm x^2\mathrm y=0\\\mathrm y(0)=\frac37\\\mathrm y\left(1\right)=?\\\frac{\mathrm{dy}}{\mathrm{dx}}=-7\mathrm x^2\mathrm y\\\frac{\mathrm{dy}}{\mathrm y}=-7\mathrm x^2\;\mathrm{dx}\\\int\frac{\mathrm{dy}}{\mathrm y}=-\int7\mathrm x^2\;\mathrm{dx}\\\ln\left(\mathrm y\right)=-\frac{7\mathrm x^3}3+\mathrm c\\\mathrm y=\mathrm{ke}^\frac{7\mathrm x^3}3\\\mathrm y\left(0\right)=\frac37=\mathrm k\left(1\right)\\\mathrm k=\frac37\\\mathrm y\left(1\right)=\frac37\mathrm e^{-7/3}\end{array}$

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