Verify that $y=e^{ax}$ is a solution of $x\dfrac{dy}{dx}=y\log y$.

Verify that y=eax is a solution of x(dy)/(dx)=ylog y.

Exercise 6.3 · Q32

y=e^{ax}

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Differentiate $y=e^{ax}$ : $\dfrac{dy}{dx}=ae^{ax}=ay$ . So $x\dfrac{dy}{dx}=axy$ . On the other hand, $\log y=\log(e^{ax})=ax$ , so $y\log y=y\cdot ax=axy$ as well. Hence $x\dfrac{dy}{dx}=y\log y$ , exactl …

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Q.Verify that $y=e^{ax}$ is a solution of $x\dfrac{dy}{dx}=y\log y$ .

Concept understanding — General and Particular Solutions of a Differential Equation

Q.Verify that y=eaxy=e^{ax}y=eax is a solution of xdydx=ylog⁡yx\dfrac{dy}{dx}=y\log yxdxdy​=ylogy.

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Q.Verify that $y=e^{ax}$ is a solution of $x\dfrac{dy}{dx}=y\log y$ .

Unlock everything free for 14 days