78.3.17 problem 5 (e)

Internal problem ID [18120]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 7 (Homogeneous Equations). Problems at page 67
Problem number : 5 (e)
Date solved : Tuesday, January 28, 2025 at 11:29:13 AM
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: 0.002 (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: 0.045 (sec). Leaf size: 20

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

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