Consider the initial value problem
y′+ (3/7)y=1-(1/3)t, y(0)=y0
- I Need Answers To All Questions Consider The Initial Value Problem Y 3 7 Y 1 1 3 T Y 0 Y0 1 (19.98 KiB) Viewed 37 times
What additional equation expresses the requirement that the solution does not cross the taxis? y′(t)=0y(t)=0y′′(t)=0
The equations found in (a) and (b) form a system of two equations for t and y0. Show how the DE can be used to solve directly for t. y′+73y=0, but also 1−71t=0, so t=7. y′+37y=0, but also 1−31t=0, so t=3. y′+73y=0, but also 1−31t=0, so t=3. y′+37y=0, but also 1−71t=0, so t=7.
Find the solution for the initial value problem with initial condition y(0)=y0(0). y=(27112)−97t+y0e−73ty=(27112)−97t+(y0−27112)e−73ty=(11227)−499t+(y0+11227)e−73ty=(27112)+349t+(y0−27112)e−73ty=−97t+(y0−27112)e37t
Finish solving the equations found in (a) and (b). y0=−499e73+27112y0=2749e79−27112y0=−2749e79+27112y0=27112e499+2749y0=−27112e349+2749