12.3.9 problem 10

Internal problem ID [1586]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number : 10
Date solved : Monday, January 27, 2025 at 05:09:30 AM
CAS classification : [_separable]

\begin{align*} \left (y-1\right )^{2} y^{\prime }&=2 x +3 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 100

dsolve((y(x)-1)^2*diff(y(x),x)=2*x+3,y(x), singsol=all)
 

\begin{align*} y &= \left (3 x^{2}+3 c_1 +9 x \right )^{{1}/{3}}+1 \\ y &= -\frac {\left (3 x^{2}+3 c_1 +9 x \right )^{{1}/{3}}}{2}-\frac {i \sqrt {3}\, \left (3 x^{2}+3 c_1 +9 x \right )^{{1}/{3}}}{2}+1 \\ y &= -\frac {\left (3 x^{2}+3 c_1 +9 x \right )^{{1}/{3}}}{2}+\frac {i \sqrt {3}\, \left (3 x^{2}+3 c_1 +9 x \right )^{{1}/{3}}}{2}+1 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.425 (sec). Leaf size: 103

DSolve[(y[x]-1)^2*D[y[x],x]==2*x+3,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 1+\sqrt [3]{3 x^2+9 x-1+3 c_1} \\ y(x)\to 1+\frac {1}{2} i \left (\sqrt {3}+i\right ) \sqrt [3]{3 x^2+9 x-1+3 c_1} \\ y(x)\to 1-\frac {1}{2} \left (1+i \sqrt {3}\right ) \sqrt [3]{3 x^2+9 x-1+3 c_1} \\ \end{align*}