76.5.31 problem 32

Internal problem ID [17451]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.7 (Substitution Methods). Problems at page 108
Problem number : 32
Date solved : Tuesday, January 28, 2025 at 10:38:43 AM
CAS classification : [_linear]

\begin{align*} \left (2-x \right ) y^{\prime }&=y+2 \left (2-x \right )^{5} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

dsolve((2-x)*diff(y(x),x)=y(x)+2*(2-x)^5,y(x), singsol=all)
 

\[ y = \frac {\frac {\left (x -2\right )^{6}}{3}+c_{1}}{x -2} \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 26

DSolve[(2-x)*D[y[x],x]==y[x]+2*(2-x)^5,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {(x-2)^6-3 c_1}{3 (2-x)} \]