2.22 problem 22

Internal problem ID [908]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {\left (-2+x \right ) \left (x -1\right ) y^{\prime }-\left (4 x -3\right ) y-\left (-2+x \right )^{3}=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 55

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

\[ y \relax (x ) = \frac {\left (x^{5}-10 x^{4}+40 x^{3}-80 x^{2}+80 x -32\right ) c_{1}}{x -1}-\frac {x^{3}-6 x^{2}+12 x -8}{2 \left (x -1\right )} \]

Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 30

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

\begin{align*} y(x)\to \frac {(x-2)^3 \left (-1+2 c_1 (x-2)^2\right )}{2 (x-1)} \\ \end{align*}