32.2.13 problem Differential equations with Linear Coefficients. Exercise 8.13, page 69

Internal problem ID [5797]
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
Date solved : Monday, January 27, 2025 at 01:19:13 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y+7+\left (2 x +y+3\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.194 (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)
 

\[ y \left (x \right ) = \left (-x^{3}+6 x^{2}-12 x +72+8 \sqrt {-2 x^{3}+12 x^{2}-24 x +80}\right )^{{1}/{3}}+\frac {\left (x -2\right )^{2}}{\left (-x^{3}+6 x^{2}-12 x +72+8 \sqrt {-2 x^{3}+12 x^{2}-24 x +80}\right )^{{1}/{3}}}-x -5 \]

✓ Solution by Mathematica

Time used: 6.801 (sec). Leaf size: 198

DSolve[{(y[x]+7)+(2*x+y[x]+3)*D[y[x],x]==0,y[0]==1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^2-\left (\sqrt [3]{-x^3+6 x^2+8 \sqrt {2} \sqrt {-x^3+6 x^2-12 x+40}-12 x+72}+4\right ) x+\left (-x^3+6 x^2+8 \sqrt {2} \sqrt {-x^3+6 x^2-12 x+40}-12 x+72\right )^{2/3}-5 \sqrt [3]{-x^3+6 x^2+8 \sqrt {2} \sqrt {-x^3+6 x^2-12 x+40}-12 x+72}+4}{\sqrt [3]{-x^3+6 x^2+8 \sqrt {2} \sqrt {-x^3+6 x^2-12 x+40}-12 x+72}} \]