Internal problem ID [4453]
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`]]
\[ \boxed {y+\left (2 x +y+3\right ) y^{\prime }=-7} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.14 (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)
\[ y \left (x \right ) = \left (-x^{3}+6 x^{2}-12 x +72+8 \sqrt {-2 x^{3}+12 x^{2}-24 x +80}\right )^{\frac {1}{3}}+\frac {\left (x -2\right )^{2}}{\left (-x^{3}+6 x^{2}-12 x +72+8 \sqrt {-2 x^{3}+12 x^{2}-24 x +80}\right )^{\frac {1}{3}}}-x -5 \]
✓ Solution by Mathematica
Time used: 6.783 (sec). Leaf size: 198
DSolve[{(y[x]+7)+(2*x+y[x]+3)*y'[x]==0,y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^2-\left (\sqrt [3]{-x^3+6 x^2+8 \sqrt {2} \sqrt {-x^3+6 x^2-12 x+40}-12 x+72}+4\right ) x+\left (-x^3+6 x^2+8 \sqrt {2} \sqrt {-x^3+6 x^2-12 x+40}-12 x+72\right )^{2/3}-5 \sqrt [3]{-x^3+6 x^2+8 \sqrt {2} \sqrt {-x^3+6 x^2-12 x+40}-12 x+72}+4}{\sqrt [3]{-x^3+6 x^2+8 \sqrt {2} \sqrt {-x^3+6 x^2-12 x+40}-12 x+72}} \]