# Differential Equation Questions Worksheet

## Differential Equation Questions Worksheet

International Association University Summer Sessions (IAUSS) Assignment 1 Differential Equation Summer Session 2020 Mr. HernΓ‘ndez Studentβs Name: 1) State the type and order of the given differential equation. Determinate whether or not the equation is linear, if nonlinear explain why? Identify the dependent and independent variables. a) π₯ b) π3 π¦ ππ¦ 4 ππ₯ ππ₯ β( ) +π¦ = 0 3 π4 π’ π2 π’ ππ₯ ππ¦ 2 +5 4 β 0.33π’ = 0 2) Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution: a) π¦ β²β² β 6π¦ β² + 13π¦ = 0; π¦ = π 3π₯ cos 2π₯ 3) Verify that the indicated expression is an implicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution: a) ππ ππ‘ = (π β 1)(1 β 2π); 2πβ1 ln ( πβ1 ) = π‘ 4) Verify that the function π(π₯ ) = π1 π π₯ + π2 π β2π₯ is a solution to the linear equation π2 π¦ ππ₯ 2 ππ¦ + ππ₯ β 2π¦ = 0, for any choice of the constants ππ and ππ . Determine ππ and ππ so that the initial condition π¦(0) = 2, π¦ β² (0) = 1 is satisfied. 5) Solve the initial value problem using βseparable variableβ ππ¦ ππ₯ π¦β1 = π₯+3 ; π¦(β1) = 0 6) Give an example of a Homogenous and a nonhomogeneous linear differential equation. 1 of 2 7) Heart Pacemaker consists of a switch, battery of constant voltage πΈ0 , a capacitor with constant capacitance πΆ, and the heart as a resistor with constant resistance R. When the switch is closed, the capacitor charges; when the switch is open, the capacitor discharges, sending an electrical stimulus to the heart. During the time the heart is being stimulated, the voltage πΈ across the heart satisfies the linear differential equation ππΈ 1 =β πΈ. ππ‘ π
πΆ Solve the DE subject to πΈ (4) = πΈ0 . 8) In the following exercises determine whether the given D.E. is exact. If itβs exact, solve it. If not, find the multiple for exactness and then solve it. a) (2π¦ β 6π₯ )ππ₯ + (3π₯ + 4π₯ 2 π¦ β1 )ππ¦ = 0 ππ¦ b) π₯ ππ₯ = 2π₯π 2 β π¦ + 6π₯ 2 9) In 1790 the population of the United States was 3.93 million, and in 1890 it was 62.98 million. Using the Malthusian model [π(π‘) = π0 π ππ‘ ], estimate the U.S. population as a function of time. Use your result to predict the population in 1900. 2 of 2 …

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