Differential equation

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Solve
x(1-x^2{})dy+(2x^2{}y-y-5x^3{})dx=0

#Mathematics #Calculus

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Ð”Ð²Ò¥Ñ—ÑuÏ now in medical c ·2009-03-04 03:50:38

put y=vx

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Ð”Ð²Ò¥Ñ—ÑuÏ now in medical c ·2009-03-04 03:58:04

x(1-x^2)dy+(2x^2vx-vx-5x^3)dx=0 \Rightarrow (1-x^2)(v+x\frac{dv}{dx})+(2vx^2-v-5x^2)=0 \Rightarrow \frac{dv}{dx}(1-x^2)=x(5-v) \Rightarrow \int \frac{dv}{5-v}=\int \frac{xdx}{1-x^2}

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Differential equation

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