10.5.5 problem 5

Internal problem ID [1197]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.6. Page 100
Problem number : 5
Date solved : Monday, January 27, 2025 at 04:43:53 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {-a x -b y}{b x +c y} \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 77

dsolve(diff(y(x),x) = (-a*x-b*y(x))/(b*x+c*y(x)),y(x), singsol=all)
 

\begin{align*} y &= \frac {-b x c_1 +\sqrt {-x^{2} \left (a c -b^{2}\right ) c_1^{2}+c}}{c c_1} \\ y &= \frac {-b x c_1 -\sqrt {-x^{2} \left (a c -b^{2}\right ) c_1^{2}+c}}{c c_1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 17.743 (sec). Leaf size: 139

DSolve[D[y[x],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*}