64.6.7 problem 7

Internal problem ID [13357]
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
Date solved : Tuesday, January 28, 2025 at 05:31:48 AM
CAS classification : [_separable]

\begin{align*} 8 x^{3} y-12 x^{3}+\left (x^{4}+1\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (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)
 

\[ y = \frac {3}{2}+\frac {c_{1}}{\left (x^{4}+1\right )^{2}} \]

✓ Solution by Mathematica

Time used: 0.056 (sec). Leaf size: 38

DSolve[(8*x^3*y[x]-12*x^3)+(1+x^4)*D[y[x],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*}