What is the solution for (dy)/(dx)(x^2+1)+7x(y-1)=0,y(0)=4 ?

The solution for (dy)/(dx)(x^2+1)+7x(y-1)=0,y(0)=4 is y= 3/((x^2+1)^{7/2)}+1

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(dy)/(dx)(x^2+1)+7x(y-1)=0,y(0)=4

\frac{d y}{d x} (x^{2} + 1) + 7 x (y - 1) = 0, y (0) = 4

y = \frac{3}{( x ^{2} + 1 ) ^{\frac{7}{2}}} + 1

Solution steps

\frac{d y}{d x} (x^{2} + 1) + 7 x (y - 1) = 0

Solve separable ODE:

y = \frac{3}{( x ^{2} + 1 ) ^{\frac{7}{2}}} + 1

y = \frac{3}{( x ^{2} + 1 ) ^{\frac{7}{2}}} + 1

\int \frac{x ^{2}}{x ^{2} + 9} d x

\frac{\partial}{\partial y} (y^{2} z)

\int \frac{3 x ^{3} + 4 x}{( x ^{2} + 1 ) ^{2}} d x

\int p^{4} e^{- p} d p

x \to - 1 lim (x^{3} - 2 x^{2} + x - 3)

What is the solution for (dy)/(dx)(x^2+1)+7x(y-1)=0,y(0)=4 ?
The solution for (dy)/(dx)(x^2+1)+7x(y-1)=0,y(0)=4 is y= 3/((x^2+1)^{7/2)}+1