- #1

karush

Gold Member

MHB

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Solve the de $$\dfrac{dy}{dx}=\dfrac{1}{7}\sqrt{y}\cos^2{\sqrt{y}}$$

sepate variables

$$\displaystyle \dfrac{dy}{\sqrt{y}\, \cos^2{\sqrt{y}} }=\dfrac{1}{7}\, dx

\implies \int{\dfrac{{d}y}{\sqrt{y}\,\cos^2{\left(\sqrt{y} \right) }} }

= \int{ \dfrac{1}{7}\,{d}x}$$

ok i think u subst is next ... maybe...

$$u=\sqrt{y} \therefore du=\dfrac{{d}y}{2\,\sqrt{y}}$$

sepate variables

$$\displaystyle \dfrac{dy}{\sqrt{y}\, \cos^2{\sqrt{y}} }=\dfrac{1}{7}\, dx

\implies \int{\dfrac{{d}y}{\sqrt{y}\,\cos^2{\left(\sqrt{y} \right) }} }

= \int{ \dfrac{1}{7}\,{d}x}$$

ok i think u subst is next ... maybe...

$$u=\sqrt{y} \therefore du=\dfrac{{d}y}{2\,\sqrt{y}}$$

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