50.5.15 problem 4(e)

Internal problem ID [7885]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.7. Homogeneous Equations. Page 28
Problem number : 4(e)
Date solved : Monday, January 27, 2025 at 03:30:59 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

dsolve((2*x+3*y(x)-1)-4*(x+1)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \left (x +1\right )^{{3}/{4}} c_{1} +2 x +3 \]

✓ Solution by Mathematica

Time used: 0.055 (sec). Leaf size: 20

DSolve[(2*x+3*y[x]-1)-4*(x+1)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 x+c_1 (x+1)^{3/4}+3 \]