12.5.25 problem 22

Internal problem ID [1649]
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 : 22
Date solved : Monday, January 27, 2025 at 05:16:11 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.050 (sec). Leaf size: 18

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

\[ y = \frac {2 x}{-2 \ln \left (x \right )-1+2 i \pi } \]

✓ Solution by Mathematica

Time used: 0.134 (sec). Leaf size: 25

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

\[ y(x)\to -\frac {2 i x}{2 i \log (x)+2 \pi +i} \]