If y(x) satisfies the differential equation y" + x²y = 0, where y(0) = yo and y'(0) = y, show that its transform Y(p) satisfies the equation Y" +p?Y = pyo + yo- %3D

Q: What are the P(x) and Q(x) of y' =y-xy³e2Xrespectively?

A: Given the differential equation is: Since

Q: (c) 2ry'y-y²+²=0.

A: 2xy'y-y2+x2=0⇒2xyy'=y2-x2

Q: Show that the transformation 2 = ln x transforms the differential equation 2 x ²³y" + Axy' + By=0…

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Q: let h(y)=(y-3y2)5(y2+2)6  h'(y) in simplified form.

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Q: Transform the differential equation 2y′′−y′+4y=e^(mt) y(0) = 2  y'(0)= 5 a )into an algebraic…

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Q: Consider the differential equations y' = x + y²,y' = x - y²₁ y² = -x - y². The slope field depicted…

A: Given differential equationsslope field are calculated by analyzing equilibrium points or nullclines

Q: Find the solution for this second ODE y(0) = 1, y'(0) = 1

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Q: -80- 60- 40 20 20 40 60 80 100 120

A: First you have to note that this piecewise function graph indicate that a lot of different functions…

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.