62.12.27 problem Ex 28

Internal problem ID [12873]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 19. Summary. Page 29
Problem number : Ex 28
Date solved : Tuesday, January 28, 2025 at 04:29:53 AM
CAS classification : [_Bernoulli]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 13

dsolve(x*diff(y(x),x)+y(x)-y(x)^2*ln(x)=0,y(x), singsol=all)
 

\[ y = \frac {1}{1+c_{1} x +\ln \left (x \right )} \]

✓ Solution by Mathematica

Time used: 0.156 (sec). Leaf size: 20

DSolve[x*D[y[x],x]+y[x]-y[x]^2*Log[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{\log (x)+c_1 x+1} \\ y(x)\to 0 \\ \end{align*}