given differential equation. Then determine a value of the con- - first verify that y(x) satisfies...

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given differential equation. Then determine a value of the con- - first verify that y(x) satisfies the stant C so that y(x) satisfies the given initial condition. Use a computer or graphing calculator (if desired) to sketch several typical solutions of the given differential equation, and high- light the one that satisfies the given initial condition. 17. y' + y = 0; y(x) = Ce*, y(0) = 2 18. y' = 2y; y(x) = Ce²t, y(0) = 3 = y +1; y(x) = Ce³-1, y(0) = 5 will 20. y'=x-y; y(x) = Ce-x + x = 1, y(0) = 10 21. y' + 3x²y = 0; y(x) = Ce-x³, y(0) = 7 22. e' y'= 1; y(x) = ln(x + C), y(0) = 0 dy 23. ..X +3y= 2x³; y(x) = x³ +Cx³, y(2) = 1b 24. xy' - 3y = x³; y(x) = x³ (C+ lnx), y(1) = 17 25. y'= 3x²(y² + 1); y(x) = tan(x³ + C), y(0) = 1 ~ y' + y tan.x = cos x; y(x) = (x + C) cos x, y(t) = 0 V co Athe given differential equation. Then determine a value of the con- - first verify that y(x) satisfies the stant C so that y(x) satisfies the given initial condition. Use a computer or graphing calculator (if desired) to sketch several typical solutions of the given differential equation, and high- light the one that satisfies the given initial condition. 17. y' + y = 0; y(x) = Ce*, y(0) = 2 18. y' = 2y; y(x) = Ce²t, y(0) = 3 = y +1; y(x) = Ce³-1, y(0) = 5 will 20. y'=x-y; y(x) = Ce-x + x = 1, y(0) = 10 21. y' + 3x²y = 0; y(x) = Ce-x³, y(0) = 7 22. e' y'= 1; y(x) = ln(x + C), y(0) = 0 dy 23. ..X +3y= 2x³; y(x) = x³ +Cx³, y(2) = 1b 24. xy' - 3y = x³; y(x) = x³ (C+ lnx), y(1) = 17 25. y'= 3x²(y² + 1); y(x) = tan(x³ + C), y(0) = 1 ~ y' + y tan.x = cos x; y(x) = (x + C) cos x, y(t) = 0 V co Athe