20.4.37 problem Problem 54

Internal problem ID [3672]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page 79
Problem number : Problem 54
Date solved : Monday, January 27, 2025 at 07:53:55 AM
CAS classification : [[_homogeneous, `class C`], _Riccati]

\begin{align*} y^{\prime }&=\left (9 x -y\right )^{2} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.101 (sec). Leaf size: 28

dsolve([diff(y(x),x)=(9*x-y(x))^2,y(0) = 0],y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (9 x -3\right ) {\mathrm e}^{6 x}+9 x +3}{1+{\mathrm e}^{6 x}} \]

✓ Solution by Mathematica

Time used: 0.154 (sec). Leaf size: 31

DSolve[{D[y[x],x]==(9*x-y[x])^2,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {9 x+e^{6 x} (9 x-3)+3}{e^{6 x}+1} \]