60.2.334 problem 911

Internal problem ID [10921]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 911
Date solved : Monday, January 27, 2025 at 10:24:18 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} y^{\prime }&=-\left (-\frac {\ln \left (y\right )}{x}+\frac {\cos \left (x \right ) \ln \left (y\right )}{\sin \left (x \right )}-\textit {\_F1} \left (x \right )\right ) y \end{align*}

✓ Solution by Maple

Time used: 0.316 (sec). Leaf size: 21

dsolve(diff(y(x),x) = -(-1/x*ln(y(x))+1/sin(x)*cos(x)*ln(y(x))-_F1(x))*y(x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{\csc \left (x \right ) x \left (c_{1} +\int \frac {f_{1} \left (x \right ) \sin \left (x \right )}{x}d x \right )} \]

✓ Solution by Mathematica

Time used: 0.737 (sec). Leaf size: 105

DSolve[D[y[x],x] == (F1[x] + Log[y[x]]/x - Cot[x]*Log[y[x]])*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^x\left (\frac {2 \log (y(x)) \sin (K[1])}{K[1]^2}+\frac {2 (\text {F1}(K[1]) \sin (K[1])-\cos (K[1]) \log (y(x)))}{K[1]}\right )dK[1]+\int _1^{y(x)}\left (-\frac {2 \sin (x)}{x K[2]}-\int _1^x\left (\frac {2 \sin (K[1])}{K[1]^2 K[2]}-\frac {2 \cos (K[1])}{K[1] K[2]}\right )dK[1]\right )dK[2]=c_1,y(x)\right ] \]