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Popular >

(x-1)((dy)/(dx))=4-y^2

Solution

(x - 1) (\frac{d y}{d x}) = 4 - y^{2}

Solution

y = - \frac{2 e ^{4 c_{1}} x ^{4}}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} + \frac{8 e ^{4 c_{1}} x ^{3}}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} - \frac{12 e ^{4 c_{1}} x ^{2}}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} + \frac{8 e ^{4 c_{1}} x}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} - \frac{2 e ^{4 c_{1}}}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} - \frac{2}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x}

Solution steps

(x - 1) (\frac{d y}{d x}) = 4 - y^{2}

Solve separable ODE:

y = - \frac{2 e ^{4 c_{1}} x ^{4}}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} + \frac{8 e ^{4 c_{1}} x ^{3}}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} - \frac{12 e ^{4 c_{1}} x ^{2}}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} + \frac{8 e ^{4 c_{1}} x}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} - \frac{2 e ^{4 c_{1}}}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} - \frac{2}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x}

y = - \frac{2 e ^{4 c_{1}} x ^{4}}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} + \frac{8 e ^{4 c_{1}} x ^{3}}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} - \frac{12 e ^{4 c_{1}} x ^{2}}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} + \frac{8 e ^{4 c_{1}} x}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} - \frac{2 e ^{4 c_{1}}}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x} - \frac{2}{1 - e ^{4 c_{1}} x ^{4} - e ^{4 c_{1}} + 4 e ^{4 c_{1}} x ^{3} - 6 e ^{4 c_{1}} x ^{2} + 4 e ^{4 c_{1}} x}

Popular Examples

(dy)/(dx)=x+4xy

\frac{d y}{d x} = x + 4 x y

xsqrt(1-y^2dx)+ysqrt(1-x^2)dy=0

x 1 - y^{2} d x + y 1 - x^{2} d y = 0

\frac{d y}{d t} - t y = y

d/(dθ)(r(θ))+r(θ)tan(θ)=tan(θ)

\frac{d}{d θ} (r (θ)) + r (θ) tan (θ) = tan (θ)

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

\frac{d y}{d x} = \frac{1 + x ^{2}}{1 - y ^{2}}, y = 0, x = 0

Frequently Asked Questions (FAQ)

What is the solution for (x-1)((dy)/(dx))=4-y^2 ?
The solution for (x-1)((dy)/(dx))=4-y^2 is