Internal problem ID [3945]
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 8.13, page
69.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y+7+\left (2 x +y+3\right ) y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 87
dsolve([(y(x)+7)+(2*x+y(x)+3)*diff(y(x),x)=0,y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \left (-x^{3}+6 x^{2}-12 x +72+8 \sqrt {-2 x^{3}+12 x^{2}-24 x +80}\right )^{\frac {1}{3}}+\frac {\left (x -2\right )^{2}}{\left (-x^{3}+6 x^{2}-12 x +72+8 \sqrt {-2 x^{3}+12 x^{2}-24 x +80}\right )^{\frac {1}{3}}}-x -5 \]
✓ Solution by Mathematica
Time used: 6.615 (sec). Leaf size: 158
DSolve[{(y[x]+7)+(2*x+y[x]+3)*y'[x]==0,y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2-\left (\sqrt [3]{8 \left (\sqrt {80-2 x ((x-6) x+12)}+9\right )-x ((x-6) x+12)}+4\right ) x+\left (8 \left (\sqrt {80-2 x ((x-6) x+12)}+9\right )-x ((x-6) x+12)\right )^{2/3}-5 \sqrt [3]{8 \left (\sqrt {80-2 x ((x-6) x+12)}+9\right )-x ((x-6) x+12)}+4}{\sqrt [3]{8 \left (\sqrt {80-2 x ((x-6) x+12)}+9\right )-x ((x-6) x+12)}} \\ \end{align*}