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|Solve the given differential equation. 7ydx - 7xdy + x" dx =4dx The solution is (Type an equation.)Find the particular solution to the given differential equation that satisfies the given conditions. x 2 + dy = 5(xdx + ydy); x= 1 when y =0 The particular solution is (Type an equation.)Use Euler's method to find y-values of the solution for the given values of x and Ax, if the curve of the solution passes through the given point. Check the results against known values by solving the differential equation exactly. dx - = 2x - 7; x= 0 to x= 1; Ax = 0.2; (0,8) Using Euler's method, complete the following table. 0.0 |0.2 10.4 0.6 10.8 |1.0 y 8.00 (Round to two decimal places as needed.)An electric circuit contains a 1-H inductor, a 2-$2 resistor, and a voltage source of sin t. The resulting differential equation relating the current i and the time t is di / dt + 2i = sin t. Find i after 0.5 s by Euler's method with At= 0.1 s if the initial current is zero. Solve the equation exactly and compare the values. Use Euler's method to find i after 0.5 s. approx =A (Round the final answer to four decimal places as needed. Round all intermediate values to nine decimal places as needed.)Find the equation of the curve for the given slope and point through which it passes. Use a graphing calculator to display the curve. Slope given by Andy; passes through (2,1) What is the equation of the curve? 2=D If interest in a bank account is compounded continuously, the amount grows at a rate that is proportional to the amount present in the account. Interest that is compounded daily very closely approximates this situation. Determine the amount in an account after one year if $1000 is placed in the account and it pays 4% interest year, compounded continuously. After 1 year the account balance will be approximately $. (Round to the nearest cent as needed.)