Find the general solution of the homogeneous differential equation {eq}y'' + 1y = 0 {/eq}
Question:
Find the general solution of the homogeneous differential equation {eq}y'' + 1y = 0 {/eq}
Differential Equation: :
It is important to note that the general solution of the differential equation of the form: {eq}ay''+by'+cy=0 {/eq} is given by: {eq}y=e^{\alpha \:t}\left(c_1\cos \left(\beta \:t\right)+c_2\sin \left(\beta \:t\right)\right) {/eq} where {eq}k_1=\alpha +i\:\beta ,\:k_2=\alpha -i\:\beta \: {/eq} Also we have: {eq}y=e^{kt} {/eq}
Answer and Explanation: 1
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In the problem, we have to find the general solution of the homogeneous differential equation {eq}y'' + y =...
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Chapter 16 / Lesson 1Discover what separable differential equations are and their uses. Learn to identify if an equation is separable and how to solve them through given examples.