28.1.122 problem 145

Internal problem ID [4428]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 145
Date solved : Monday, January 27, 2025 at 09:16:59 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} y+2 y^{3} y^{\prime }&=\left (x +4 y \ln \left (y\right )\right ) y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.081 (sec). Leaf size: 27

dsolve(y(x)+2*y(x)^3*diff(y(x),x)=(x+4*y(x)*ln(y(x)))*diff(y(x),x),y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left (2 \,{\mathrm e}^{\textit {\_Z}} \textit {\_Z}^{2}-{\mathrm e}^{3 \textit {\_Z}}+c_{1} {\mathrm e}^{\textit {\_Z}}-x \right )} \]

✓ Solution by Mathematica

Time used: 0.169 (sec). Leaf size: 28

DSolve[y[x]+2*y[x]^3*D[y[x],x]==(x+4*y[x]*Log[y[x]])*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x=y(x) \left (2 \log ^2(y(x))-y(x)^2\right )+c_1 y(x),y(x)\right ] \]