y'+y^2 sin x = 0, y(0)=1 2xy + (1+y)y' = 0, y(2)=1 y' = 2xy - x^2 y', y(-3)=1 y' + 2xy = xe^{-2x^2}, y(0)=1 y' - 4y = 2e^{3x} + 3e^{2x}, y(0)=5 y' - 3y = e^{3x}, y(0)=4 y' + (2/x)y = x^3, y(1)=-1 xy' + y = ln x, y(1)=3 y' - cos x y = -3 cos x, y(0)=1 y''

Решите следующие дифференциальные уравнения.\( y^{\prime}+y^{2} \sin x=0, \quad y(0)=1 \)1.\( 2 x y+(1+y) y^{\prime}=0, \quad y(2)=1 \)2.\( y^{\prime}=2 x y-x^{2} y^{\prime}, \quad y(-3)=1 \)3.\( y^{\prime}+2 x y=x e^{-2 x^{2}}, \quad y(0)=1 \)4.\( y^{\prime}-4 y=2 e^{3 x}+3 e^{2 x}, \quad y(0)=5 \)5.\( y^{\prime}-3 y=e^{3 x}, \quad y(0)=4 \)6.\( y^{\prime}+\frac{2}{x} y=x^{3}, \quad y(1)=-1 \)7.\( x y^{\prime}+y=\ln x, \quad y(1)=3 \)8.\( y^{\prime}-\cos x y=-3 \cos x, \quad y(0)=1 \)9.\( y^{\prime \prime}=x, \quad y(0)=1, y^{\prime}(0)=2 \)10.\( y^{\prime \prime}-2 y^{\prime}+y=x^{2}-3 x+4, \quad y(0)=2, y^{\prime}(0)=-1 \)Совет: \( y_{1}=a x^{2}+b x+c \)11.\( y^{\prime \prime}-4 y^{\prime}-5 y=\sin 5 x \quad y(0)=1, y^{\prime}(0)=3 \)Совет: \( y_{1}=a \sin 5 x+b \cos 5 x \)12.\( y^{\prime \prime}+\omega^{2} y=0, \quad y(0)=3, y^{\prime}(0)=2 \)