Internal problem ID [3942]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 8
Problem number: Differential equations with Linear Coefficients. Exercise 8.10, page
69.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _exact, _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {3 x -2 y+4-\left (2 x +7 y-1\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.3 (sec). Leaf size: 38
dsolve((3*x-2*y(x)+4)-(2*x+7*y(x)-1)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {11}{25}-\frac {\frac {2 \left (25 x +26\right ) c_{1}}{7}+\frac {\sqrt {25 \left (25 x +26\right )^{2} c_{1}^{2}+7}}{7}}{25 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.101 (sec). Leaf size: 63
DSolve[(3*x-2*y[x]+4)-(2*x+7*y[x]-1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{7} \left (-2 x-\sqrt {x (25 x+52)+1+49 c_1}+1\right ) \\ y(x)\to \frac {1}{7} \left (-2 x+\sqrt {x (25 x+52)+1+49 c_1}+1\right ) \\ \end{align*}