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Student Support Forum > General > > "DSolve and initial value problems"

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Please answer this:6+3 =



Original Message (ID '71492') By Bill Simpson:
I am guessing that some variable was set to some value after your first DSolve and before your second. With a brand new fresh open notebook I try your example and get In[1]:= DSolve[{y''[t]+4 y'[t]+4 y[t]==Sin[t],y[0]==0},y[t],t] Out[1]= {{y[t] -> -(-4 - 25*t*C[2] + 4*E^(2*t)*Cos[t] - 3*E^(2*t)*Sin[t])/(25*E^(2*t))}} In[2]:= Simplify[%] Out[2]= {{y[t] -> (4/E^(2*t) + (25*t*C[2])/E^(2*t) - 4*Cos[t] + 3*Sin[t])/25}} And then try your initial conditions and get In[3]:= DSolve[{y''[t]+4 y'[t]+4 y[t]==Sin[t],y[0]==1,y'[0]==0},y[t],t] Out[3]= {{y[t] -> -(-29 - 55*t + 4*E^(2*t)*Cos[t] - 3*E^(2*t)*Sin[t])/(25*E^(2*t))}} In[4]:= Simplify[%] Out[4]= {{y[t] -> (29/E^(2*t) + (55*t)/E^(2*t) - 4*Cos[t] + 3*Sin[t])/25}} Try a fresh start and see if you can reproduce this.