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solve the d.e.6C) 9y"-12y+4=0
發問:
solve the d.e. , 9y"-12y+4=0 , when x=0, y=5 and y'=10 thanks....
solve the d.e. 9y"-12y+4=0 , when x=0, y=5 and y'=10 Sol: Aided Eq. m^2-12=0 => m=+-2√3Homogenous solution: yh(x)=a*e^(2√3x)+b*e^(-2√3x)Particular solution: yp(x)=c*x^2+f*x+gyp'=2cx+fyp"=2c9yp"-12y=18c-12(cx^2+fx+g)=-12cx^2-12fx+(18c-12g)=-4c=0, f=0 18c-12g=-4 => g=4/12=1/3=> yp(x)=1/3General solution: y(x)=yh(x)+yp(x)=a*e^(2√3x)+b*e^(-2√3x)+1/3Initial coditions: y(0)=a+b+1/3=5 => a+b=14/3y'(x)=2√3a*e^(2√3x)-2√3b*e^(-2√3x)y'(0)=2√3a-2√3b=10 => a-b=5√3/3Add: a=(14+5√3)/6Subtract: b=(14-5√3)/6Final solution: y(x)=[(14+5√3)/6]*e^(2√3x)+[(14-5√3)/6]*e^(-2√3x)+1/3
其他解答:
solve the d.e.6C) 9y"-12y+4=0
發問:
solve the d.e. , 9y"-12y+4=0 , when x=0, y=5 and y'=10 thanks....
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最佳解答:solve the d.e. 9y"-12y+4=0 , when x=0, y=5 and y'=10 Sol: Aided Eq. m^2-12=0 => m=+-2√3Homogenous solution: yh(x)=a*e^(2√3x)+b*e^(-2√3x)Particular solution: yp(x)=c*x^2+f*x+gyp'=2cx+fyp"=2c9yp"-12y=18c-12(cx^2+fx+g)=-12cx^2-12fx+(18c-12g)=-4c=0, f=0 18c-12g=-4 => g=4/12=1/3=> yp(x)=1/3General solution: y(x)=yh(x)+yp(x)=a*e^(2√3x)+b*e^(-2√3x)+1/3Initial coditions: y(0)=a+b+1/3=5 => a+b=14/3y'(x)=2√3a*e^(2√3x)-2√3b*e^(-2√3x)y'(0)=2√3a-2√3b=10 => a-b=5√3/3Add: a=(14+5√3)/6Subtract: b=(14-5√3)/6Final solution: y(x)=[(14+5√3)/6]*e^(2√3x)+[(14-5√3)/6]*e^(-2√3x)+1/3
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