Internal problem ID [881]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 1, Introduction. Section 1.2 Page 14
Problem number: 5(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x^{2}-2 x^{2} y+2}{x^{3}}=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (1) = {\frac {3}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve([diff(y(x),x) = (x^2-2*x^2*y(x)+2)/x^3,y(1) = 3/2],y(x), singsol=all)
\[ y \relax (x ) = \frac {\frac {x^{2}}{2}+2 \ln \relax (x )+1}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 19
DSolve[{y'[x] ==(x^2-2*x^2*y[x]+2)/x^3,y[1]==3/2},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{x^2}+\frac {2 \log (x)}{x^2}+\frac {1}{2} \\ \end{align*}