64.5.25 problem 25

Internal problem ID [13338]
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 : 25
Date solved : Tuesday, January 28, 2025 at 05:22:50 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} y^{\prime }+\frac {y}{2 x}&=\frac {x}{y^{3}} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.103 (sec). Leaf size: 17

dsolve([diff(y(x),x)+y(x)/(2*x)=x/y(x)^3,y(1) = 2],y(x), singsol=all)
 

\[ y = \sqrt {\frac {\sqrt {x^{4}+15}}{x}} \]

✓ Solution by Mathematica

Time used: 0.261 (sec). Leaf size: 20

DSolve[{D[y[x],x]+y[x]/(2*x)==x/y[x]^3,{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\sqrt [4]{x^4+15}}{\sqrt {x}} \]