What is the solution for 3e^{7x}(dy)/(dx)=-49 x/(y^2),y(0)=1 ?

The solution for 3e^{7x}(dy)/(dx)=-49 x/(y^2),y(0)=1 is y=\sqrt[3]{7xe^{-7x}+e^{-7x}}

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3e^{7x}(dy)/(dx)=-49 x/(y^2),y(0)=1

3 e^{7 x} \frac{d y}{d x} = - 49 \frac{x}{y ^{2}}, y (0) = 1

y = 3 7 x e^{- 7 x} + e^{- 7 x}

Solution steps

3 e^{7 x} \frac{d y}{d x} = - 49 \frac{x}{y ^{2}}

Solve separable ODE:

y = 3 7 x e^{- 7 x} + e^{- 7 x}

y = 3 7 x e^{- 7 x} + e^{- 7 x}

a y d x + x d y = 0

y^{^{'}} 2 y = 3 e^{4 x} - 4 sin (4 x), y (0) = - 5

3 y \cdot d x - x \cdot d y = 0

y^{^{'}} (t) = \frac{t}{( 1 + y ^{2} )}, y (0) = 0

y d x + (x - 9) d y = 0, y (10) = 49

What is the solution for 3e^{7x}(dy)/(dx)=-49 x/(y^2),y(0)=1 ?
The solution for 3e^{7x}(dy)/(dx)=-49 x/(y^2),y(0)=1 is y=\sqrt[3]{7xe^{-7x}+e^{-7x}}