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Problem: Find the general solution of the equation \( x y^{\prime \prime}+ \) \( +2 y^{\prime}+x y=0 \), if the function \( (\sin x) / x \) is its particular solution. clip2net.com

8.1.2.15 Second order differential equations

2 $

Problem: Find the general solution of the equation (1\( \left.-x^{2}\right) y^{\prime \prime}-2 x y^{\prime}+2 y=0 \), if the function \( x \) is its particular solution. clip2net.com

8.1.2.16 Second order differential equations

2 $

Problem: Solve the following equation using the method of variation of arbitrary constant: \[ y^{\prime \prime}+4 y=\frac{1}{\sin ^{2} x} \text {. } \]

8.1.2.17 Second order differential equations

1.75 $

Problem: Solve the following equation by the method of variation of arbitrary constant: \[ y^{\prime \prime}+4 y^{\prime}+4 y=e^{-2 x} \ln x \text {. } \]

8.1.2.20 Second order differential equations

1.75 $

Problem: For the given inhomogeneous differential equation \( y^{\prime \prime}+16 y=\sin (4 x+\alpha), \quad(\alpha= \) const \( ) \) write the form of its particular solution with indefinite coefficients (don't find the numerical values of the coefficients).

8.1.2.21 Second order differential equations

0.75 $

Problem: For the given inhomogeneous differential equation \( y^{\prime \prime}-4 y^{\prime}=2 \cos ^{2} 4 x \) write the form of its particular solution with indefinite coefficients (don't find the numerical values of the coefficients). clip2net.com

8.1.2.22 Second order differential equations

1 $

Problem: Find the general solution of the equation: \[ y^{\prime \prime}-y=\operatorname{ch} x \text {. } \]

8.1.2.23 Second order differential equations

1 $

Problem: Find the general solution of Euler's equation: \[ x^{2} y^{\prime \prime}+x y^{\prime}+y=0 \text {. } \]

8.1.2.24 Second order differential equations

2 $

Problem: Find the general solution of Euler's equation: \( x^{2} y^{\prime \prime}+x y^{\prime}+4 y=10 x \).

8.1.2.25 Second order differential equations

2 $

Problem: Find the general solution of Euler's equation: \[ (2 x+1)^{2} y^{\prime \prime}-2(2 x+1) y^{\prime}+4 y=0 \text {. } \] clip2net.com

8.1.2.27 Second order differential equations

2.5 $

Problem: Find the particular solution of the second order differential equation, satisfying given initial conditions: \[ y^{\prime \prime}=\sqrt{1-\left(y^{\prime}\right)^{2}}, \quad y(0)=-1, \quad y^{\prime}(0)=0 . \] clip2net.com

8.1.2.28 Second order differential equations

1.5 $

Problem: Find the general solution of the differential equation: \[ y^{\prime \prime \prime}-3 y^{\prime \prime}-y^{\prime}+3 y=(4-8 x) e^{x} \text {. } \]

8.1.3.1 Higher order differential equations

1.5 $

Problem: Find the general solution of the equation \( x^{3} y^{\prime \prime \prime}+ \) \( +5 x^{2} y^{\prime \prime}+2 x y^{\prime}-2 y=0 \), if its two particular solutions are known \( y_{1}=x \) and \( y_{2}=1 / x \). clip2net.com

8.1.3.2 Higher order differential equations

3.75 $

Problem: Investigate linear dependence for the following system of functions: \( \sin 2 x, \sin x, \cos x \). clip2net.com

8.1.3.3 Higher order differential equations

0.75 $

Problem: Investigate linear dependence for the following system of functions: \( x, 2 x, x^{2} \).

8.1.3.4 Higher order differential equations

0 $

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