Question

6 (a) Solve the \( \mathrm{DE}\left(D^{2}-2 D+5\right) y=e^{2 x} \sin x \) by operator method. (b) By the method of variation of parameters to solve \( y^{\prime \prime}-2 y^{\prime}+y=x e^{x} \ln x \).

          6 (a) Solve the \( \mathrm{DE}\left(D^{2}-2 D+5\right) y=e^{2 x} \sin x \) by operator method.
(b) By the method of variation of parameters to solve \( y^{\prime \prime}-2 y^{\prime}+y=x e^{x} \ln x \).

6 (a) Solve the DE(D^2-2 D+5) y=e^2 xsin x by operator method.
(b) By the method of variation of parameters to solve y^''-2 y^'+y=x e^xln x.

Added by Joshua L.

Differential Equations and Linear Algebra

Stephen W. Goode, Scott A. Annin 4th Edition

Chapter 8

Instant Answer

Solved by Expert Sriram Soundarrajan

07/10/2020

Step 1

The roots of this equation are \(1 \pm 2i\), so the complementary function is \(y_c = e^x(A\cos(2x) + B\sin(2x))\). Show more…

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Question

6 (a) Solve the \( \mathrm{DE}\left(D^{2}-2 D+5\right) y=e^{2 x} \sin x \) by operator method. (b) By the method of variation of parameters to solve \( y^{\prime \prime}-2 y^{\prime}+y=x e^{x} \ln x \).

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