80.3.3 problem 3

Internal problem ID [18547]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 29. Problems at page 81
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 11:57:08 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 a x +b y+\left (2 c y+b x +e \right ) y^{\prime }&=g \end{align*}

✓ Solution by Maple

Time used: 0.105 (sec). Leaf size: 90

dsolve((2*a*x+b*y(x))+(2*c*y(x)+b*x+e)*diff(y(x),x)=g,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {-\sqrt {-64 \left (a c -\frac {b^{2}}{4}\right ) \left (\left (a x -\frac {g}{2}\right ) c -\frac {b \left (b x +e \right )}{4}\right )^{2} c_{1}^{2}+4 c}+\left (-4 a b c x +b^{3} x -4 a c e +b^{2} e \right ) c_{1}}{8 \left (a c -\frac {b^{2}}{4}\right ) c c_{1}} \]

✓ Solution by Mathematica

Time used: 17.046 (sec). Leaf size: 132

DSolve[(2*a*x+b*y[x])+(2*c*y[x]+b*x+e)*D[y[x],x]==g,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\frac {\sqrt {\frac {4 c x (g-a x)+b^2 x^2+2 b e x+4 c^2 c_1+e^2}{c}}}{\sqrt {\frac {1}{c}}}+b x+e}{2 c} \\ y(x)\to -\frac {-\frac {\sqrt {\frac {4 c x (g-a x)+b^2 x^2+2 b e x+4 c^2 c_1+e^2}{c}}}{\sqrt {\frac {1}{c}}}+b x+e}{2 c} \\ \end{align*}