12.5.27 problem 24

Internal problem ID [1651]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable Equations. Section 2.4 Page 68
Problem number : 24
Date solved : Monday, January 27, 2025 at 05:17:50 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} x y y^{\prime }+x^{2}+y^{2}&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 18

dsolve([x*y(x)*diff(y(x),x)+x^2+y(x)^2=0,y(1) = 2],y(x), singsol=all)
 

\[ y = \frac {\sqrt {-2 x^{4}+18}}{2 x} \]

✓ Solution by Mathematica

Time used: 0.192 (sec). Leaf size: 25

DSolve[{x*y[x]*D[y[x],x]+x^2+y[x]^2==0,y[1]==2},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\sqrt {9-x^4}}{\sqrt {2} x} \]