Internal problem ID [547]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.6. Page 100
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y^{\prime }-\frac {-a x -b y}{b x +c y}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 83
dsolve(diff(y(x),x) = (-a*x-b*y(x))/(b*x+c*y(x)),y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {b x c_{1} -\sqrt {-a c \,c_{1}^{2} x^{2}+b^{2} c_{1}^{2} x^{2}+c}}{c c_{1}} y \left (x \right ) = -\frac {b x c_{1} +\sqrt {-a c \,c_{1}^{2} x^{2}+b^{2} c_{1}^{2} x^{2}+c}}{c c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 17.783 (sec). Leaf size: 139
DSolve[y'[x]== (-a*x-b*y[x])/(b*x+c*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {b x+\sqrt {-a c x^2+b^2 x^2+c e^{2 c_1}}}{c} y(x)\to \frac {-b x+\sqrt {b^2 x^2+c \left (-a x^2+e^{2 c_1}\right )}}{c} y(x)\to -\frac {\sqrt {x^2 \left (b^2-a c\right )}+b x}{c} y(x)\to \frac {\sqrt {x^2 \left (b^2-a c\right )}-b x}{c} \end{align*}