8.4.23 problem 23

Internal problem ID [726]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 23
Date solved : Monday, January 27, 2025 at 02:59:19 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

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

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

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