Internal problem ID [1945]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 8, page 34
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {b_{1} y+\left (b_{1} x +b_{2} y+c_{2} \right ) y^{\prime }=-a_{1} x -c_{1}} \]
✓ Solution by Maple
Time used: 0.328 (sec). Leaf size: 80
dsolve((a__1*x+b__1*y(x)+c__1)+(b__1*x+b__2*y(x)+c__2)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\sqrt {-\left (a_{1} b_{2} -b_{1}^{2}\right ) \left (\left (a_{1} x +c_{1} \right ) b_{2} -b_{1}^{2} x -c_{2} b_{1} \right )^{2} {\mathrm e}^{2 c_{1}}+b_{2}}\, {\mathrm e}^{-c_{1}}-\left (a_{1} b_{2} -b_{1}^{2}\right ) \left (b_{1} x +c_{2} \right )}{\left (a_{1} b_{2} -b_{1}^{2}\right ) b_{2}} \]
✓ Solution by Mathematica
Time used: 16.604 (sec). Leaf size: 106
DSolve[(a1*x+b1*y[x]+c1)+(b1*x+b2*y[x]+c2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\frac {\sqrt {-x (\text {a1} x+2 \text {c1})+\frac {(\text {b1} x+\text {c2})^2}{\text {b2}}+\text {b2} c_1}}{\sqrt {\frac {1}{\text {b2}}}}+\text {b1} x+\text {c2}}{\text {b2}} \\ y(x)\to -\frac {\text {b1} x+\text {c2}}{\text {b2}}+\sqrt {\frac {1}{\text {b2}}} \sqrt {-x (\text {a1} x+2 \text {c1})+\frac {(\text {b1} x+\text {c2})^2}{\text {b2}}+\text {b2} c_1} \\ \end{align*}