Solve :dy/dx=y3/(e2x-y2)

Consider dx/dydx/dy = (e2x–y2)/y3Put ex=tgives, exdx/dy = dt/dySo, dt/dy = t3/y3 – t/yNow, let t=vyso, dt/dy = v+ydv/dy gives, v+ydv/dy=v3-vtherefore, ∫dv/(v3-2v) = ∫dv/v(v+rt2)(v-rt2) = ∫dy/yNow you can solve it can’t you..just by partial fractions.

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Grade 12Integral Calculus

Solve :
dy/dx=y³/(e^2x-y²)

Harsh

11 Years agoGrade 12

1 Answer

Yash Jain

11 Years ago

Consider dx/dy
dx/dy = (e^2x–y²)/y³
Put e^x=t
gives, e^xdx/dy = dt/dy
So, dt/dy = t³/y³ – t/y
Now, let t=vy
so, dt/dy = v+ydv/dy
gives, v+ydv/dy=v³-v
therefore, ∫dv/(v³-2v) = ∫dv/v(v+rt2)(v-rt2) = ∫dy/y
Now you can solve it can’t you..
just by partial fractions.