12.1.13 problem 5(b)

Internal problem ID [1531]
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)
Date solved : Monday, January 27, 2025 at 04:59:01 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (1\right )&={\frac {3}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.008 (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)
 

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

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 19

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

\[ y(x)\to \frac {1}{x^2}+\frac {2 \log (x)}{x^2}+\frac {1}{2} \]