Let o(x) = -t2 dt, x E R. e (i) e=t* dt = Y[o(b) –o(a)]. Show that a (ii) Show that the function y = o(x)ez satisfies the differential equation dy/dx = 2xy+2/VT.

Q: Consider the differential equation x²y" 4xy' + 6y=0; x², x³, (0, 0). Verify that the given functions…

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Q: Let g(x) - [₁6'd -3 g'(x) = -0 6t²dt. Find g'(x).

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Q: which of the following expressions is equivalent to: 3cot^2(t)/csc(t)   a. 3-3cos^2(t)/cos(t) b.…

A: This question is related to trignometry, We will solve it using trignometric identities.

Q: 3. Write the exact differential: f(x,y)=e-y-el-

A: Given- fx,y=ex-y-ey-x To write the exact differential.

Q: Consider the scalar differential equation d Define the potential V(x) by Use the chain rule to show…

A: Note: We will be solving part (H2) only as asked.Given that .Define potential function  defined as…

Q: Let h(x) = [² Find h' (1). tln(t² +e-1)dt.

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Q: Show that y = x+vx +1 satisfies the differential equation (x + 1)°Y + x°Y. ydy -m³y 0 + X- dx2 dx

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Q: Find the particular solution to the differential equation (x-2) dy = xy that dx passes through the…

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Q: Let y 3x². = Find the change in y, Ay when x = 1 and Ax = 0.4 Find the differential dy when x = 1…

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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.