4.25 Problems 1201 to 1250

   4.25.1 \(y''(x)-a^2 y(x)=x+1\)
   4.25.2 \(y''(x)=a x+b y(x)\)
   4.25.3 \(a^2 y(x)+y''(x)=x^2+x+1\)
   4.25.4 \(a^2 y(x)+y''(x)=\cos (b x)\)
   4.25.5 \(a^2 y(x)+y''(x)=\cot (a x)\)
   4.25.6 \(a^2 y(x)+y''(x)=\sin (b x)\)
   4.25.7 \(y''(x)+x y(x)=0\)
   4.25.8 \(y(x) (a+b x)+y''(x)=0\)
   4.25.9 \(\left (a+x^2\right ) y(x)+y''(x)=0\)
   4.25.10 \(\left (a-x^2\right ) y(x)+y''(x)=0\)
   4.25.11 \(y''(x)=\left (a+x^2\right ) y(x)\)
   4.25.12 \(y(x) \left (a+b^2 x^2\right )+y''(x)=0\)
   4.25.13 \(y(x) \left (a+b x+c x^2\right )+y''(x)=0\)
   4.25.14 \(y(x) \left (\text {a0}+\text {a1} x^2+x^4\right )+y''(x)=0\)
   4.25.15 \(a x^k y(x)+y''(x)=0\)
   4.25.16 \(y(x) \left (\text {a0}+\text {a1} x+\text {a2} x^2+\text {a3} x^3+\text {a4} x^4+x^8\right )+y''(x)=0\)
   4.25.17 \(y(x) (a+b \cos (2 x))+y''(x)=0\)
   4.25.18 \(y(x) (a+b \cos (2 x)+k \cos (4 x))+y''(x)=0\)
   4.25.19 \(y(x) \left (\sum _{n=0}^m a(n) \cos (2 n x)\right )+y''(x)=0\)
   4.25.20 \(y''(x)=2 y(x) \csc ^2(x)\)
   4.25.21 \(a y(x) \csc ^2(x)+y''(x)=0\)
   4.25.22 \(y(x) \left (\text {a0}+\text {a1} \cos ^2(x)+\text {a2} \csc ^2(x)\right )+y''(x)=0\)
   4.25.23 \(y''(x)=y(x) \left (a^2+(p-1) p \csc ^2(x)+(q-1) q \sec ^2(x)\right )\)
   4.25.24 \(y(x) \left (a+b \sin ^2(x)\right )+y''(x)=0\)
   4.25.25 \(y''(x)=y(x) \left (2 \tan ^2(x)+1\right )\)
   4.25.26 \(y''(x)-y(x) \left (a^2-b e^x\right )=0\)
   4.25.27 \(y''(x)-\left (a^2-e^{2 x}\right ) y(x)=0\)
   4.25.28 \(y(x) \left (a+b e^x+c e^{2 x}\right )+y''(x)=0\)
   4.25.29 \(a e^{b x} y(x)+y''(x)=0\)
   4.25.30 \(y(x) \left (a+b \cosh ^2(x)\right )+y''(x)=0\)
   4.25.31 \(y(x) \left (a+b \sinh ^2(x)\right )+y''(x)=0\)
   4.25.32 \(y(x) \left (a+b \sin ^2(x)\right )+y''(x)=0\)
   4.25.33 \(\frac {(a+b) y(x)}{x^2}+y''(x)=0\)
   4.25.34 \(y''(x)-y'(x)+x y(x)=0\)
   4.25.35 \(y''(x)+2 y'(x)+y(x)=0\)
   4.25.36 \(y''(x)-2 y'(x)+y(x)=(x-6) x^2\)
   4.25.37 \(y''(x)-2 y'(x)+y(x)=e^x\)
   4.25.38 \(y''(x)-2 y'(x)+y(x)=e^x \left (3 x^2+2 x+1\right )\)
   4.25.39 \(y''(x)-2 y'(x)+y(x)=e^x \sin (x)\)
   4.25.40 \(y''(x)+2 y'(x)+y(x)=x^2+3 e^{2 x}-\cos (x)\)
   4.25.41 \(y''(x)-2 y'(x)+y(x)=8 e^{3 x} x^2\)
   4.25.42 \(y''(x)-2 y'(x)+y(x)=50 \cos (x) \cosh (x)\)
   4.25.43 \(y''(x)+2 y'(x)+3 y(x)=0\)
   4.25.44 \(y''(x)+2 y'(x)+y(x)=e^{-x} \cos (x)\)
   4.25.45 \(y''(x)+2 y'(x)+5 y(x)=0\)
   4.25.46 \(y''(x)+2 y'(x)+5 y(x)=8 \sinh (x)\)
   4.25.47 \(-2 \tan (a) y'(x)+\csc ^2(a) y(x)+y''(x)=0\)
   4.25.48 \(-2 \tan (a) y'(x)+\csc ^2(a) y(x)+y''(x)=x^2 e^{x \tan (a)}\)
   4.25.49 \(y''(x)+3 y'(x)+2 y(x)=0\)
   4.25.50 \(y''(x)+3 y'(x)+2 y(x)=\cos (a x)\)