56.1.67 problem 67

Internal problem ID [8779]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 67
Date solved : Monday, January 27, 2025 at 04:50:12 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} 3 y y^{\prime \prime }+y&=5 \end{align*}

✓ Solution by Maple

Time used: 0.041 (sec). Leaf size: 59

dsolve(3*y(x)*diff(y(x),x$2)+y(x)=5,y(x), singsol=all)
 

\begin{align*} -3 \left (\int _{}^{y}\frac {1}{\sqrt {30 \ln \left (\textit {\_a} \right )+9 c_{1} -6 \textit {\_a}}}d \textit {\_a} \right )-x -c_{2} &= 0 \\ 3 \left (\int _{}^{y}\frac {1}{\sqrt {30 \ln \left (\textit {\_a} \right )+9 c_{1} -6 \textit {\_a}}}d \textit {\_a} \right )-x -c_{2} &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.330 (sec). Leaf size: 41

DSolve[3*y[x]*D[y[x],{x,2}]+y[x]==5,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{y(x)}\frac {1}{\sqrt {c_1+\frac {2}{3} (5 \log (K[1])-K[1])}}dK[1]{}^2=(x+c_2){}^2,y(x)\right ] \]