Find the real-valued solution to the initial value problem {y′1y′2==−3y1−2y2,5y1+3y2,y1(0)=3,y 2(0)=−10. {y1′=−3y1−2y2,y1(0)=3,y2′=5y1+3y2,y 2(0)=−10. use tt as the independent variable in your answers.

Given that



Then:



The eigenvectors are as follows:



Therefore, the solution is given as follows:



Thus, the solution is given by:



Applying the initial condition, we have



Therefore, the solution to the initial value problem is:

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