一阶常微分方程[img=152x26]1802e4d6075ee4f.png[/img]的通解为
A: sin(2*t)/5-cos(2*t)/10+C*exp(-4*t)
B: sin(2*t)/7+cos(2*t)/5-C*exp(-3*t)
C: sin(2*t)/7-C*cos(2*t)/10+C*exp(-2*t)
D: sin(2*t)/7-cos(2*t)/7+C*exp(-5*t)
A: sin(2*t)/5-cos(2*t)/10+C*exp(-4*t)
B: sin(2*t)/7+cos(2*t)/5-C*exp(-3*t)
C: sin(2*t)/7-C*cos(2*t)/10+C*exp(-2*t)
D: sin(2*t)/7-cos(2*t)/7+C*exp(-5*t)
举一反三
- 求微分方程[img=269x55]17da6536a9fba07.png[/img]的通解； （ ） A: (C15*sin(2*t))/exp(3*t) + (C16*sin(2*t))/exp(3*t) B: (C15*cos(2*t))/exp(3*t) - (C16*sin(2*t))/exp(3*t) C: (C15*cos(2*t))/exp(3*t) + (C16*cos(2*t))/exp(3*t) D: (C15*cos(2*t))/exp(3*t) + (C16*sin(2*t))/exp(3*t)
- 设\(z = {e^{x - 2y}}\)，而\(x = \sin t\)，\(y = {t^3}\)，则全导数\( { { dz} \over {dt}} = \) A: \({e^{\sin t - {t^3}}}(\cos t - 6{t^2})\) B: \({e^{\sin t - 2{t^3}}}(\sin t - 6{t^2})\) C: \({e^{\cos t - 2{t^3}}}(\cos t - 6{t^2})\) D: \({e^{\sin t - 2{t^3}}}(\cos t - 6{t^2})\)
- 用Matlab求解常微分方程初值问题[img=191x61]1802e4db6ff00c5.png[/img]，输出结果是： A: 2*exp(t)+4*t*exp(-t)+1 B: 2*exp(-t)+4*t*exp(-t)-1 C: 2*exp(-t)+4*t*exp(-t)+1 D: 2*exp(t)+4*t*exp(-t)-1
- 求微分方程[img=364x55]17da65386dfd612.png[/img]的通解； （ ） A: - cos(2*x)*exp(x)*(x/4 - sin(4*x)/16) + C23*cos(2*x)*exp(x) + C24*sin(2*x)*exp(x) B: (3*sin(2*x)*exp(x))/32 - (sin(6*x)*exp(x))/32 - cos(2*x)*exp(x)*(x/4 - sin(4*x)/16) + C23*cos(2*x)*exp(x) + C24*sin(2*x)*exp(x) C: - sin(4*x)/16) + C23*cos(2*x)*exp(x) + C24*sin(2*x)*exp(x) D: (sin(6*x)*exp(x))/32 - cos(2*x)*exp(x)*(x/4 - sin(4*x)/16) + C23*cos(2*x)*exp(x) + C24*sin(2*x)*exp(x)
- 设\(z = {e^{x - 2y}}\)，而\(x = \sin t,\;y = {t^3},\)则\( { { dz} \over {dt}} = \)( ) A: \({e^{\sin t - 2{t^3}}}\) B: \({e^{\sin t - 2{t^3}}}\left( {\cos t - 6{t^2}} \right)\) C: \({e^{\sin t - 2{t^3}}}\ {\sin t } \) D: \({e^{\sin t - 2{t^3}}}\,{t^3}\)