Solve the initial-value problemdydx=cosx,y(0)=1.𝑑𝑦𝑑𝑥=cos𝑥,𝑦(0)=1.Select one:a.y=−sinx+1𝑦=−sin𝑥+1b.y=sinx+1𝑦=sin𝑥+1c.y=tanx+1𝑦=tan𝑥+1d.y=cosx+1
Question
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
Similar Questions
Solve the initial-value problemdydx=cosx,y(0)=1.𝑑𝑦𝑑𝑥=cos𝑥,𝑦(0)=1.Select one:a.y=−sinx+1𝑦=−sin𝑥+1b.y=sinx+1𝑦=sin𝑥+1c.y=tanx+1𝑦=tan𝑥+1d.y=cosx+1
Find the solution to the initial value problemy′−e−t+5y=−5, y(0)=−1.𝑦′−𝑒−𝑡+5𝑦=−5, 𝑦(0)=−1.
What is the equation of a line through (-1, 4) and (-2, 7)?Question 27Select one:a.y = 3x + 1b.y = -3x + 1c.y = -3x + 7d.y = 3x + 7e.None of these
Determine the domain of the functiony=|x+2|−1𝑦=|𝑥+2|−1.Select one:A.x⩾−7𝑥⩾−7B.y⩾−1𝑦⩾−1C.y∈R𝑦∈𝑅D.x∈R
Solve the differential equation 𝑑 𝑦 𝑑 𝑥 = 2 𝑥 dx dy =2x with initial condition 𝑦 ( 0 ) = 3 y(0)=3.