64.5.17 problem 17

Internal problem ID [13330]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 17
Date solved : Tuesday, January 28, 2025 at 05:22:32 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 92

dsolve(diff(y(x),x)+(4*y(x)-8/y(x)^3)*x=0,y(x), singsol=all)
 

\begin{align*} y &= \left (2 \,{\mathrm e}^{8 x^{2}}+c_{1} \right )^{{1}/{4}} {\mathrm e}^{-2 x^{2}} \\ y &= -\left (2 \,{\mathrm e}^{8 x^{2}}+c_{1} \right )^{{1}/{4}} {\mathrm e}^{-2 x^{2}} \\ y &= -i \left (2 \,{\mathrm e}^{8 x^{2}}+c_{1} \right )^{{1}/{4}} {\mathrm e}^{-2 x^{2}} \\ y &= i \left (2 \,{\mathrm e}^{8 x^{2}}+c_{1} \right )^{{1}/{4}} {\mathrm e}^{-2 x^{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.954 (sec). Leaf size: 145

DSolve[D[y[x],x]+(4*y[x]-8/y[x]^3)*x==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt [4]{2+e^{-8 x^2+4 c_1}} \\ y(x)\to -i \sqrt [4]{2+e^{-8 x^2+4 c_1}} \\ y(x)\to i \sqrt [4]{2+e^{-8 x^2+4 c_1}} \\ y(x)\to \sqrt [4]{2+e^{-8 x^2+4 c_1}} \\ y(x)\to -\sqrt [4]{2} \\ y(x)\to -i \sqrt [4]{2} \\ y(x)\to i \sqrt [4]{2} \\ y(x)\to \sqrt [4]{2} \\ \end{align*}