Internal problem ID [11681]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, Miscellaneous Review. Exercises page 60
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {8 y x^{3}+\left (x^{4}+1\right ) y^{\prime }=12 x^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve((8*x^3*y(x)-12*x^3)+(1+x^4)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {3}{2}+\frac {c_{1}}{\left (x^{4}+1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 38
DSolve[(8*x^3*y[x]-12*x^3)+(1+x^4)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {3 x^8+6 x^4+2 c_1}{2 \left (x^4+1\right )^2} \\ y(x)\to \frac {3}{2} \\ \end{align*}