Find the solution for the initial value problem with initial condition y(0) = yo (0).521652y =+-t+ ( yo273272727t+ (yo +52y =-5216524y =2752452일+(yole27y =-27452y = --t + ( yo9.27Finish solving the equations found in (a) and (b).16 252+27Yo= --275216e 16 +279Yo =27529e4 +163Yo = -2716 252Yo =e 427-2752163 +2716Yoe27의 Consider the initial value problemy+y=1-. (0) == yo -What equation expresses the requirement that the solution touches the t-axis?c y(t) = 0y (t) = 0O y (t)= 0What additional equation expresses the requirement that the solution does not cross the t-axis?C y' (t) = 0O y(t) = 0C y (t) = 0The equations found in (a) and (b) form a system of two equations for t and yo. Show how the DE can be used to solve directly for t.3+Gy = 0, but also 1 –1t = 0, so t = 4.3y' +-y = 0, but also 1 - t1= 0, so t = 3.y +4= 0, but also 1– zt1= 0, so t = 3.34= 0, but also 1 -1= 0, so t = 4.3

The given differential equation is first order linear differential equation. We solve it by finding…

Find the solution for the initial value problem with initial condition y(0) = yo (0). 52 16 52 y = + -t+ ( yo 27 3 27 27 27 t+ (yo + 52 y = - 52 16 52 4 y = 27 52 4 52 일+(yo le 27 y = - 27 4 52 y = - -t + ( yo 9. 27 Finish solving the equations found in (a) and (b). 16 2 52 + 27 Yo = -- 27 52 16 e 16 + 27 9 Yo = 27 52 9 e4 + 16 3 Yo = - 27 16 2 52 Yo = e 4 27 - 27 52 16 3 + 27 16 Yo e 27 의

Find the solution for the initial value problem with initial condition y(0) = yo (0). 52 16 52 y = + -t+ ( yo 27 3 27 27 27 t+ (yo + 52 y = - 52 16 52 4 y = 27 52 4 52 일+(yo le 27 y = - 27 4 52 y = - -t + ( yo 9. 27 Finish solving the equations found in (a) and (b). 16 2 52 + 27 Yo = -- 27 52 16 e 16 + 27 9 Yo = 27 52 9 e4 + 16 3 Yo = - 27 16 2 52 Yo = e 4 27 - 27 52 16 3 + 27 16 Yo e 27 의

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Find the solution for the initial value problem with initial condition y(0) = yo (0).
52
16
52
y =
+
-t+ ( yo
27
3
27
27
27
t+ (yo +
52
y =
-
52
16
52
4
y =
27
52
4
52
일+(yo
le
27
y =
-
27
4
52
y = -
-t + ( yo
9.
27
Finish solving the equations found in (a) and (b).
16 2
52
+
27
Yo
= --
27
52
16
e 16 +
27
9
Yo =
27
52
9
e4 +
16
3
Yo = -
27
16 2
52
Yo =
e 4
27
-
27
52
16
3 +
27
16
Yo
e
27
의

Consider the initial value problem
y+y=1-. (0) =
= yo -
What equation expresses the requirement that the solution touches the t-axis?
c y(t) = 0
y (t) = 0
O y (t)
= 0
What additional equation expresses the requirement that the solution does not cross the t-axis?
C y' (t) = 0
O y(t) = 0
C y (t) = 0
The equations found in (a) and (b) form a system of two equations for t and yo. Show how the DE can be used to solve directly for t.
3
+Gy = 0, but also 1 –
1
t = 0, so t = 4.
3
y' +
-y = 0, but also 1 - t
1
= 0, so t = 3.
y +
4
= 0, but also 1– zt
1
= 0, so t = 3.
3
4
= 0, but also 1 -
1
= 0, so t = 4.
3

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