Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Verify that the function {y}={c}_{{1}}{e}^{{{a}{x}}}{{{b}}}{x}

Question

Verify that the function $y = c_{1} e^{a x} cos b x + c_{2} e^{a x} sin b x$ , where $c_{1}, c_{2}$ are arbitrary constants is a solution of the differential equation. $\frac{d ^{2} y}{d x ^{2}} - 2 a \frac{d y}{d x} + (a^{2} + b^{2}) y = 0$

Views: 722 students

Found 4 tutors discussing this question

Sofia Discussed

Verify that the function

y = c_{1} e^{a x} cos b x + c_{2} e^{a x} sin b x

, where

c_{1}, c_{2}

are arbitrary constants is a solution of the differential equation.

\frac{d ^{2} y}{d x ^{2}} - 2 a \frac{d y}{d x} + (a^{2} + b^{2}) y = 0

7 mins ago

Discuss this question LIVE

7 mins ago

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our math tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text

Verify that the function

y = c_{1} e^{a x} cos b x + c_{2} e^{a x} sin b x

, where

c_{1}, c_{2}

are arbitrary constants is a solution of the differential equation.

\frac{d ^{2} y}{d x ^{2}} - 2 a \frac{d y}{d x} + (a^{2} + b^{2}) y = 0

Filo tutor solution