Solve the initial-value problemdydx=cosx,y(0)=1.𝑑𝑦𝑑𝑥=cos⁡𝑥,𝑦(0)=1.Select one:a.y=−sinx+1𝑦=−sin⁡𝑥+1b.y=sinx+1𝑦=sin⁡𝑥+1c.y=tanx+1𝑦=tan⁡𝑥+1d.y=cosx+1

Question

Solve the initial-value problemdydx=cosx,y(0)=1.𝑑𝑦𝑑𝑥=cos⁡𝑥,𝑦(0)=1.Select one:a.y=−sinx+1𝑦=−sin⁡𝑥+1b.y=sinx+1𝑦=sin⁡𝑥+1c.y=tanx+1𝑦=tan⁡𝑥+1d.y=cosx+1
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Solution 1

The given differential equation is dy/dx = cos(x), with the initial condition y(0) = 1.

Step 1: Integrate both sides of the equation with respect to x.

∫dy = ∫cos(x) dx

This gives us y = sin(x) + C, where C is the constant of integration.

Step 2: Use the initial condition to find the value of C Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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