12.2.22 problem 22

Internal problem ID [1558]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number : 22
Date solved : Monday, January 27, 2025 at 05:00:03 AM
CAS classification : [_linear]

\begin{align*} \left (x -2\right ) \left (x -1\right ) y^{\prime }-\left (4 x -3\right ) y&=\left (x -2\right )^{3} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

dsolve((x-2)*(x-1)*diff(y(x),x) -(4*x-3)*y(x)=(x-2)^3,y(x), singsol=all)
 

\[ y = \frac {2 \left (-\frac {1}{2}+\left (x -2\right )^{2} c_1 \right ) \left (x -2\right )^{3}}{2 x -2} \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 30

DSolve[(x-2)*(x-1)*D[y[x],x] -(4*x-3)*y[x]==(x-2)^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {(x-2)^3 \left (-1+2 c_1 (x-2)^2\right )}{2 (x-1)} \]