Marcus tried to solve the differential equation $$\frac{d y}{d x}=\frac{1}{3 x^{2} y^{2}}$$. This is his work: $$\frac{d y}{d x}=\frac{1}{3 x^{2} y^{2}}$$ Step 1 : $$\int 3 y^{2} d y=\int \frac{1}{x^{2}} d x $$ Step 2 :$$y^{3}=-\frac{1}{x}+C$$ Step 3 : ![](http://admin.getprephub.com/media/editor/Screenshot%202022-11-07%20104939_20221107052014035732.png) Is Marcus's work correct? If not, what is his mistake?

Here, $$\frac{d y}{d x}=\frac{1}{3 x^{2} y^{2}} $$ $$\text { or. } \int 3 y^{2} d y=\int \frac{d x}{x^{2}} $$ $$\text { or, } y^{3}=-\frac{1}{x}+C $$ $$\text { or, }$$ ![](http://admin.getprephub.com/media/editor/Screenshot%202022-11-11%20142924_20221111085949272493.png) So, $$y$$ is not equal to ![](http://admin.getprephub.com/media/editor/Screenshot%202022-11-07%20104939_20221107052014035732.png) Step $$3$$ is Wrong.

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Marcus tried to solve the differential equation $\frac{d y}{d x}=\frac{1}{3 x^{2} y^{2}}$ . This is his work:

$\frac{d y}{d x}=\frac{1}{3 x^{2} y^{2}}$

Step 1 : $\int 3 y^{2} d y=\int \frac{1}{x^{2}} d x$

Step 2 : $y^{3}=-\frac{1}{x}+C$

Step 3 :

Is Marcus’s work correct? If not, what is his mistake?

Step 3 is incorrect. The right hand side of the equalion should be

Marcus’s Work is correct

Step 1 is wrong.

Step 2 is wrong.

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